This method allows direct implementation of functions defined by mathematical induction and recursive divide and conquer algorithms.

However, that particular case is a theorem of the Zermelo—Fraenkel set theory without the axiom of choice ZF ; it is easily proved by mathematical induction.

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step).

The definition of inductive reasoning described in this article excludes mathematical induction, which is a form of deductive reasoning that is used to strictly prove properties of recursively defined sets.

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the induction).

The definition of inductive reasoning described in this article excludes mathematical induction, which is a form of deductive reasoning that is used to strictly prove properties of recursively defined sets.[7]

Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the induction).

The definition of inductive reasoning described in this article excludes mathematical inductionwhich is Accepted and discarded knowledge essay form of deductive reasoning that is used to strictly prove properties of recursively defined sets.

(A formal proof for all finite sets would use the principle of mathematical induction to prove "for every natural number k, every family of k nonempty sets has a choice function.")

It's called the principle of mathematical induction.

This is called the principle of mathematical induction.

is known as the principle of mathematical induction.